Can you please outline the answers with the corresponding letter for each question thanks A rectangular storage container with an open top is to have a capacity of 111 in³. The length of this base is 3 times the width. What should the dimensions of the container be to minimize the construction cost? Round your answers to two decimal places, if necessary.Let \( x \) be the width (in inches) of the base of the container, and \( h \) be the height (in inches) of the container.\[ x = \_\_\_\_\_\_ \text{ in} \]Complete the following parts.(a) Give a function \( f \) in the variable \( x \) for the quantity to be optimized.\[ f(x) = \_\_\_\_\_\_ \](b) State the domain of this function. (Enter your answer using interval notation.)\[ \_\_\_\_\_\_ \](c) Give the formula for \( h \) in terms of \( x \).\[ h = \_\_\_\_\_\_ \](d) To determine the optimal value of the function \( f \), we need the critical numbers.(e) These critical numbers are as follows. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)\[ x = \_\_\_\_\_\_ \]

Given that: Capacity of container, V=111 in3Length of container = 3 times widthLet L=Length of container.Let x = width of base.Let h=height of container. According to question: L=3xNow, Lhx=111Or, (3x)hx=111Or, 3hx2=111Or, x=1113h in(a)Now, area of the storage container should be minimized to minimize to construction cost.Area of container, A=Lx+2hx+2LhOr, A=3x2+8hxOr, A=3x2+8.1113xOr, f(x)=3x2+8883x(b)Domain of the function: (-∞, 0)U(0, ∞)(c)We have: 3hx2=111Or, h=1113x2(d)To obtain the cirtical values of f, we need the critical numbers of f'.(e)f'(x)=6x-8883x2Now, f'(x)=0Or, 6x-8883x2=0Or, 18x3-888=0Or, x=888181/3=3.668